If a set of matrix representation $\{M(g)\}$ for a group $G$ is irreducible, what can we say about their determinant for every $g\in G$? Are they all of non-zero determinant?
Thank you very much!
Cheers, Collin
P.S.: I'm a physics graduate student. So please use as little math terminology as possible, I would really appreciate that!
The inverse of $M(g)$ is $M(g^{-1})$.
And of course, invertible matrices have non-zero determinant.
Note that this is true for all representations, not just irreducible ones.